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Title: Control problems with vanishing Lie Bracket arising from complete odd circulant evolutionary games
We study an optimal control problem arising from a generalization of rock-paper-scissors in which the number of strategies may be selected from any positive odd number greater than 1 and in which the payoff to the winner is controlled by a control variable \begin{document}$$ \gamma $$\end{document}. Using the replicator dynamics as the equations of motion, we show that a quasi-linearization of the problem admits a special optimal control form in which explicit dynamics for the controller can be identified. We show that all optimal controls must satisfy a specific second order differential equation parameterized by the number of strategies in the game. We show that as the number of strategies increases, a limiting case admits a closed form for the open-loop optimal control. In performing our analysis we show necessary conditions on an optimal control problem that allow this analytic approach to function.  more » « less
Award ID(s):
1932991
PAR ID:
10317095
Author(s) / Creator(s):
;
Date Published:
Journal Name:
Journal of Dynamics & Games
Volume:
0
Issue:
0
ISSN:
2164-6066
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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